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O B J E C T I V E S
Heat transfer is a basic science that deals with the rate of transfer of ther-mal energy. This introductory text is intended for use in a first course inheat transfer for undergraduate engineering students, and as a reference
book for practicing engineers. The objectives of this text are
• To cover the basic principles of heat transfer.
• To present a wealth of real-world engineering applications to give stu-
dents a feel for engineering practice.
• To develop an intuitive understanding of the subject matter by empha-
sizing the physics and physical arguments.
Students are assumed to have completed their basic physics and calculus se-
quence. The completion of first courses in thermodynamics, fluid mechanics,
and differential equations prior to taking heat transfer is desirable. The rele-
vant concepts from these topics are introduced and reviewed as needed.
In engineering practice, an understanding of the mechanisms of heat trans-
fer is becoming increasingly important since heat transfer plays a crucial role
in the design of vehicles, power plants, refrigerators, electronic devices, build-
ings, and bridges, among other things. Even a chef needs to have an intuitive
understanding of the heat transfer mechanism in order to cook the food “right”
by adjusting the rate of heat transfer. We may not be aware of it, but we al-
ready use the principles of heat transfer when seeking thermal comfort. We in-
sulate our bodies by putting on heavy coats in winter, and we minimize heat
gain by radiation by staying in shady places in summer. We speed up the cool-
ing of hot food by blowing on it and keep warm in cold weather by cuddling
up and thus minimizing the exposed surface area. That is, we already use heat
transfer whether we realize it or not.
G E N E R A L A P P R O A C H
This text is the outcome of an attempt to have a textbook for a practically ori-
ented heat transfer course for engineering students. The text covers the stan-
dard topics of heat transfer with an emphasis on physics and real-world
applications, while de-emphasizing intimidating heavy mathematical aspects.
This approach is more in line with students’ intuition and makes learning the
subject matter much easier.
The philosophy that contributed to the warm reception of the first edition of
this book has remained unchanged. The goal throughout this project has been
to offer an engineering textbook that
P R E F A C E
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• Talks directly to the minds of tomorrow’s engineers in a simple yet pre-
cise manner.
• Encourages creative thinking and development of a deeper understand-
ing of the subject matter.
• Is read by students with interest and enthusiasm rather than being used
as just an aid to solve problems.
Special effort has been made to appeal to readers’ natural curiosity and to help
students explore the various facets of the exciting subject area of heat transfer.
The enthusiastic response we received from the users of the first edition all
over the world indicates that our objectives have largely been achieved.
Yesterday’s engineers spent a major portion of their time substituting values
into the formulas and obtaining numerical results. However, now formula ma-
nipulations and number crunching are being left to computers. Tomorrow’s
engineer will have to have a clear understanding and a firm grasp of the basic
principles so that he or she can understand even the most complex problems,
formulate them, and interpret the results. A conscious effort is made to em-
phasize these basic principles while also providing students with a look at
how modern tools are used in engineering practice.
N E W I N T H I S E D I T I O N
All the popular features of the previous edition are retained while new ones
are added. The main body of the text remains largely unchanged except that
the coverage of forced convection is expanded to three chapters and the cov-
erage of radiation to two chapters. Of the three applications chapters, only the
Cooling of Electronic Equipment is retained, and the other two are deleted to
keep the book at a reasonable size. The most significant changes in this edi-
tion are highlighted next.
EXPANDED COVERAGE OF CONVECTION
Forced convection is now covered in three chapters instead of one. In Chapter
6, the basic concepts of convection and the theoretical aspects are introduced.
Chapter 7 deals with the practical analysis of external convection while Chap-
ter 8 deals with the practical aspects of internal convection. See the Content
Changes and Reorganization section for more details.
ADDITIONAL CHAPTER ON RADIATION
Radiation is now covered in two chapters instead of one. The basic concepts
associated with thermal radiation, including radiation intensity and spectral
quantities, are covered in Chapter 11. View factors and radiation exchange be-
tween surfaces through participating and nonparticipating media are covered
in Chapter 12. See the Content Changes and Reorganization section for more
details.
TOPICS OF SPECIAL INTEREST
Most chapters now contain a new end-of-chapter optional section called
“Topic of Special Interest” where interesting applications of heat transfer are
discussed. Some existing sections such as A Brief Review of Differential
Equations in Chapter 2, Thermal Insulation in Chapter 7, and Controlling Nu-
merical Error in Chapter 5 are moved to these sections as topics of special
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interest. Some sections from the two deleted chapters such as the Refrigera-
tion and Freezing of Foods, Solar Heat Gain through Windows, and Heat
Transfer through the Walls and Roofs are moved to the relevant chapters as
special topics. Most topics selected for these sections provide real-world
applications of heat transfer, but they can be ignored if desired without a loss
in continuity.
COMPREHENSIVE PROBLEMS WITH PARAMETRIC STUDIES
A distinctive feature of this edition is the incorporation of about 130 compre-
hensive problems that require conducting extensive parametric studies, using
the enclosed EES (or other suitable) software. Students are asked to study the
effects of certain variables in the problems on some quantities of interest, to
plot the results, and to draw conclusions from the results obtained. These
problems are designated by computer-EES and EES-CD icons for easy recog-
nition, and can be ignored if desired. Solutions of these problems are given in
the Instructor’s Solutions Manual.
CONTENT CHANGES AND REORGANIZATION
With the exception of the changes already mentioned, the main body of the
text remains largely unchanged. This edition involves over 500 new or revised
problems. The noteworthy changes in various chapters are summarized here
for those who are familiar with the previous edition.
• In Chapter 1, surface energy balance is added to Section 1-4. In a new
section Problem-Solving Technique, the problem-solving technique is
introduced, the engineering software packages are discussed, and
overviews of EES (Engineering Equation Solver) and HTT (Heat Trans-
fer Tools) are given. The optional Topic of Special Interest in this chap-
ter is Thermal Comfort.
• In Chapter 2, the section A Brief Review of Differential Equations is
moved to the end of chapter as the Topic of Special Interest.
• In Chapter 3, the section on Thermal Insulation is moved to Chapter 7,
External Forced Convection, as a special topic. The optional Topic of
Special Interest in this chapter is Heat Transfer through Walls and
Roofs.
• Chapter 4 remains mostly unchanged. The Topic of Special Interest in
this chapter is Refrigeration and Freezing of Foods.
• In Chapter 5, the section Solutions Methods for Systems of Algebraic
Equations and the FORTRAN programs in the margin are deleted, and
the section Controlling Numerical Error is designated as the Topic of
Special Interest.
• Chapter 6, Forced Convection, is now replaced by three chapters: Chap-
ter 6 Fundamentals of Convection,where the basic concepts of convec-
tion are introduced and the fundamental convection equations and
relations (such as the differential momentum and energy equations and
the Reynolds analogy) are developed; Chapter 7 External Forced Con-
vection, where drag and heat transfer for flow over surfaces, including
flow over tube banks, are discussed; and Chapter 8 Internal Forced
Convection, where pressure drop and heat transfer for flow in tubes are
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presented. Reducing Heat Transfer through Surfaces is added to Chap-
ter 7 as the Topic of Special Interest.
• Chapter 7 (now Chapter 9) Natural Convection is completely rewritten.
The Grashof number is derived from a momentum balance on a differ-
ential volume element, some Nusselt number relations (especially those
for rectangular enclosures) are updated, and the section Natural Con-
vection from Finned Surfaces is expanded to include heat transfer from
PCBs. The optional Topic of Special Interest in this chapter is Heat
Transfer through Windows.
• Chapter 8 (now Chapter 10) Boiling and Condensation remained largely
unchanged. The Topic of Special Interest in this chapter is Heat Pipes.
• Chapter 9 is split in two chapters: Chapter 11 Fundamentals of Thermal
Radiation, where the basic concepts associated with thermal radiation,
including radiation intensity and spectral quantities, are introduced, and
Chapter 12 Radiation Heat Transfer, where the view factors and radia-
tion exchange between surfaces through participating and nonparticipat-
ing media are discussed. The Topic of Special Interest are Solar Heat
Gain through Windows in Chapter 11, and Heat Transfer from the Hu-
man Body in Chapter 12.
• There are no significant changes in the remaining three chapters of Heat
Exchangers, Mass Transfer, and Cooling of Electronic Equipment.
• In the appendices, the values of the physical constants are updated; new
tables for the properties of saturated ammonia, refrigerant-134a, and
propane are added; and the tables on the properties of air, gases, and liq-
uids (including liquid metals) are replaced by those obtained using EES.
Therefore, property values in tables for air, other ideal gases, ammonia,
refrigerant-134a, propane, and liquids are identical to those obtained
from EES.
L E A R N I N G T O O L S
EMPHASIS ON PHYSICS
A distinctive feature of this book is its emphasis on the physical aspects of
subject matter rather than mathematical representations and manipulations.
The author believes that the emphasis in undergraduate education should re-
main on developing a sense of underlying physical mechanism and a mastery
of solving practical problems an engineer is likely to face in the real world.
Developing an intuitive understanding should also make the course a more
motivating and worthwhile experience for the students.
EFFECTIVE USE OF ASSOCIATION
An observant mind should have no difficulty understanding engineering sci-
ences. After all, the principles of engineering sciences are based on our every-
day experiences and experimental observations. A more physical, intuitive
approach is used throughout this text. Frequently parallels are drawn between
the subject matter and students’ everyday experiences so that they can relate
the subject matter to what they already know. The process of cooking, for ex-
ample, serves as an excellent vehicle to demonstrate the basic principles of
heat transfer.
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SELF-INSTRUCTING
The material in the text is introduced at a level that an average student can
follow comfortably. It speaks to students, not over students. In fact, it is self-
instructive. Noting that the principles of sciences are based on experimental
observations, the derivations in this text are based on physical arguments, and
thus they are easy to follow and understand.
EXTENSIVE USE OF ARTWORK
Figures are important learning tools that help the students “get the picture.”
The text makes effective use of graphics. It contains more figures and illus-
trations than any other book in this category. Figures attract attention and
stimulate curiosity and interest. Some of the figures in this text are intended to
serve as a means of emphasizing some key concepts that would otherwise go
unnoticed; some serve as paragraph summaries.
CHAPTER OPENERS AND SUMMARIES
Each chapter begins with an overview of the material to be covered and its re-
lation to other chapters. A summary is included at the end of each chapter for
a quick review of basic concepts and important relations.
NUMEROUS WORKED-OUT EXAMPLES
Each chapter contains several worked-out examples that clarify the material
and illustrate the use of the basic principles. An intuitive and systematic ap-
proach is used in the solution of the example problems, with particular atten-
tion to the proper use of units.
A WEALTH OF REAL-WORLD END-OF-CHAPTER PROBLEMS
The end-of-chapter problems are grouped under specific topics in the order
they are covered to make problem selection easier for both instructors and stu-
dents. The problems within each group start with concept questions, indicated
by “C,” to check the students’ level of understanding of basic concepts. The
problems under Review Problems are more comprehensive in nature and are
not directly tied to any specific section of a chapter. The problems under the
Design and Essay Problems title are intended to encourage students to make
engineering judgments, to conduct independent exploration of topics of inter-
est, and to communicate their findings in a professional manner. Several eco-
nomics- and safety-related problems are incorporated throughout to enhance
cost and safety awareness among engineering students. Answers to selected
problems are listed immediately following the problem for convenience to
students.
A SYSTEMATIC SOLUTION PROCEDURE
A well-structured approach is used in problem solving while maintaining an
informal conversational style. The problem is first stated and the objectives
are identified, and the assumptions made are stated together with their justifi-
cations. The properties needed to solve the problem are listed separately. Nu-
merical values are used together with their units to emphasize that numbers
without units are meaningless, and unit manipulations are as important as
manipulating the numerical values with a calculator. The significance of the
findings is discussed following the solutions. This approach is also used
consistently in the solutions presented in the Instructor’s Solutions Manual.
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A CHOICE OF SI ALONE OR SI / ENGLISH UNITS
In recognition of the fact that English units are still widely used in some in-
dustries, both SI and English units are used in this text, with an emphasis on
SI. The material in this text can be covered using combined SI/English units
or SI units alone, depending on the preference of the instructor. The property
tables and charts in the appendices are presented in both units, except the ones
that involve dimensionless quantities. Problems, tables, and charts in English
units are designated by “E” after the number for easy recognition, and they
can be ignored easily by the SI users.
CONVERSION FACTORS
Frequently used conversion factors and the physical constants are listed on the
inner cover pages of the text for easy reference.
S U P P L E M E N T S
These supplements are available to the adopters of the book.
COSMOS SOLUTIONS MANUAL
Available to instructors only.
The detailed solutions for all text problems will be delivered in our
new electronic Complete Online Solution Manual Organization System
(COSMOS). COSMOS is a database management tool geared towards as-
sembling homework assignments, tests and quizzes. No longer do instructors
need to wade through thick solutions manuals and huge Word files. COSMOS
helps you to quickly find solutions and also keeps a record of problems as-
signed to avoidduplication in subsequent semesters. Instructors can contact
their McGraw-Hill sales representative at http://www.mhhe.com/catalogs/rep/
to obtain a copy of the COSMOS solutions manual.
EES SOFTWARE
Developed by Sanford Klein and William Beckman from the University of
Wisconsin–Madison, this software program allows students to solve prob-
lems, especially design problems, and to ask “what if” questions. EES (pro-
nounced “ease”) is an acronym for Engineering Equation Solver. EES is very
easy to master since equations can be entered in any form and in any order.
The combination of equation-solving capability and engineering property data
makes EES an extremely powerful tool for students.
EES can do optimization, parametric analysis, and linear and nonlinear re-
gression and provides publication-quality plotting capability. Equations can be
entered in any form and in any order. EES automatically rearranges the equa-
tions to solve them in the most efficient manner. EES is particularly useful for
heat transfer problems since most of the property data needed for solving such
problems are provided in the program. For example, the steam tables are im-
plemented such that any thermodynamic property can be obtained from a
built-in function call in terms of any two properties. Similar capability is pro-
vided for many organic refrigerants, ammonia, methane, carbon dioxide, and
many other fluids. Air tables are built-in, as are psychrometric functions and
JANAF table data for many common gases. Transport properties are also pro-
vided for all substances. EES also allows the user to enter property data or
functional relationships with look-up tables, with internal functions written
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with EES, or with externally compiled functions written in Pascal, C, C��,
or FORTRAN.
The Student Resources CD that accompanies the text contains the Limited
Academic Version of the EES program and the scripted EES solutions of about
30 homework problems (indicated by the “EES-CD” logo in the text). Each
EES solution provides detailed comments and on-line help, and can easily be
modified to solve similar problems. These solutions should help students
master the important concepts without the calculational burden that has been
previously required.
HEAT TRANSFER TOOLS (HTT)
One software package specifically designed to help bridge the gap between
the textbook fundamentals and commercial software packages is Heat Trans-
fer Tools, which can be ordered “bundled” with this text (Robert J. Ribando,
ISBN 0-07-246328-7). While it does not have the power and functionality of
the professional, commercial packages, HTT uses research-grade numerical
algorithms behind the scenes and modern graphical user interfaces. Each
module is custom designed and applicable to a single, fundamental topic in
heat transfer.
BOOK-SPECIFIC WEBSITE
The book website can be found at www.mhhe.com/cengel/. Visit this site for
book and supplement information, author information, and resources for fur-
ther study or reference. At this site you will also find PowerPoints of selected
text figures.
A C K N O W L E D G M E N T S
I would like to acknowledge with appreciation the numerous and valuable
comments, suggestions, criticisms, and praise of these academic evaluators:
PREFACE
xxiv
Sanjeev Chandra
University of Toronto, Canada
Fan-Bill Cheung
The Pennsylvania State University
Nicole DeJong
San Jose State University
David M. Doner
West Virginia University Institute of
Technology
Mark J. Holowach
The Pennsylvania State University
Mehmet Kanoglu
Gaziantep University, Turkey
Francis A. Kulacki
University of Minnesota
Sai C. Lau
Texas A&M University
Joseph Majdalani
Marquette University
Jed E. Marquart
Ohio Northern University
Robert J. Ribando
University of Virginia
Jay M. Ochterbeck
Clemson University
James R. Thomas
Virginia Polytechnic Institute and
State University
John D. Wellin
Rochester Institute of Technology
cen58933_fm.qxd 9/11/2002 10:56 AM Page xxiv
Their suggestions have greatly helped to improve the quality of this text. I also
would like to thank my students who provided plenty of feedback from their
perspectives. Finally, I would like to express my appreciation to my wife
Zehra and my children for their continued patience, understanding, and sup-
port throughout the preparation of this text.
Yunus A. Çengel
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Preface xviii
Nomenclature xxvi
C H A P T E R O N E
BASICS OF HEAT TRANSFER 1
1-1 Thermodynamics and Heat Transfer 2
Application Areas of Heat Transfer 3
Historical Background 3
1-2 Engineering Heat Transfer 4
Modeling in Heat Transfer 5
1-3 Heat and Other Forms of Energy 6
Specific Heats of Gases, Liquids, and Solids 7
Energy Transfer 9
1-4 The First Law of Thermodynamics 11
Energy Balance for Closed Systems (Fixed Mass) 12
Energy Balance for Steady-Flow Systems 12
Surface Energy Balance 13
1-5 Heat Transfer Mechanisms 17
1-6 Conduction 17
Thermal Conductivity 19
Thermal Diffusivity 23
1-7 Convection 25
1-8 Radiation 27
1-9 Simultaneous Heat Transfer Mechanisms 30
1-10 Problem-Solving Technique 35
A Remark on Significant Digits 37
Engineering Software Packages 38
Engineering Equation Solver (EES) 39
Heat Transfer Tools (HTT) 39
Topic of Special Interest:
Thermal Comfort 40
Summary 46
References and Suggested Reading 47
Problems 47
C H A P T E R T W O
HEAT CONDUCTION EQUATION 61
2-1 Introduction 62
Steady versus Transient Heat Transfer 63
Multidimensional Heat Transfer 64
Heat Generation 66
2-2 One-Dimensional 
Heat Conduction Equation 68
Heat Conduction Equation in a Large Plane Wall 68
Heat Conduction Equation in a Long Cylinder 69
Heat Conduction Equation in a Sphere 71
Combined One-Dimensional 
Heat Conduction Equation 72
2-3 General Heat Conduction Equation 74
Rectangular Coordinates 74
Cylindrical Coordinates 75
Spherical Coordinates 76
2-4 Boundary and Initial Conditions 77
1 Specified Temperature Boundary Condition 78
2 Specified Heat Flux Boundary Condition 79
3 Convection Boundary Condition 81
4 Radiation Boundary Condition 82
5 Interface Boundary Conditions 83
6 Generalized Boundary Conditions 84
2-5 Solution of Steady One-Dimensional
Heat Conduction Problems 86
2-6 Heat Generation in a Solid 97
2-7 Variable Thermal Conductivity, k(T) 104
Topic of Special Interest:
A Brief Review of Differential Equations 107
Summary 111
References and Suggested Reading 112
Problems 113
C H A P T E R T H R E E
STEADY HEAT CONDUCTION 127
3-1 Steady Heat Conduction in Plane Walls 128
The Thermal Resistance Concept 129
C O N T E N T S
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CONTENTS
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Thermal Resistance Network 131
Multilayer Plane Walls 133
3-2 Thermal Contact Resistance 138
3-3 Generalized Thermal Resistance Networks 143
3-4 Heat Conduction in Cylinders and Spheres 146
Multilayered Cylinders and Spheres 148
3-5 Critical Radius of Insulation 153
3-6 Heat Transfer from Finned Surfaces 156
Fin Equation 157
Fin Efficiency 160
Fin Effectiveness 163
Proper Length of a Fin 165
3-7 Heat Transfer in Common Configurations 169
Topic of Special Interest:
Heat Transfer Through Walls and Roofs 175
Summary 185
References and Suggested Reading 186
Problems 187
C H A P T E R F O U R
TRANSIENT HEAT CONDUCTION 209
4-1 Lumped System Analysis 210
Criteria for Lumped System Analysis 211
Some Remarks on Heat Transfer in Lumped Systems 213
4-2 Transient Heat Conduction in 
Large Plane Walls, Long Cylinders, 
and Spheres with Spatial Effects 216
4-3 Transient Heat Conduction in 
Semi-Infinite Solids 228
4-4 Transient Heat Conduction in
Multidimensional Systems 231
Topic of Special Interest:
Refrigeration and Freezing of Foods 239
Summary 250
References and Suggested Reading 251
Problems 252
C H A P T E R F I V E
NUMERICAL METHODS 
IN HEAT CONDUCTION 265
5-1 Why Numerical Methods? 266
1 Limitations 267
2 Better Modeling 267
3 Flexibility 268
4 Complications 268
5Human Nature 268
5-2 Finite Difference Formulation of
Differential Equations 269
5-3 One-Dimensional Steady Heat Conduction 272
Boundary Conditions 274
5-4 Two-Dimensional 
Steady Heat Conduction 282
Boundary Nodes 283
Irregular Boundaries 287
5-5 Transient Heat Conduction 291
Transient Heat Conduction in a Plane Wall 293
Two-Dimensional Transient Heat Conduction 304
Topic of Special Interest:
Controlling Numerical Error 309
Summary 312
References and Suggested Reading 314
Problems 314
C H A P T E R S I X
FUNDAMENTALS OF CONVECTION 333
6-1 Physical Mechanism on Convection 334
Nusselt Number 336
6-2 Classification of Fluid Flows 337
Viscous versus Inviscid Flow 337
Internal versus External Flow 337
Compressible versus Incompressible Flow 337
Laminar versus Turbulent Flow 338
Natural (or Unforced) versus Forced Flow 338
Steady versus Unsteady (Transient) Flow 338
One-, Two-, and Three-Dimensional Flows 338
6-3 Velocity Boundary Layer 339
Surface Shear Stress 340
6-4 Thermal Boundary Layer 341
Prandtl Number 341
6-5 Laminar and Turbulent Flows 342
Reynolds Number 343
6-6 Heat and Momentum Transfer 
in Turbulent Flow 343
6-7 Derivation of Differential 
Convection Equations 345
Conservation of Mass Equation 345
Conservation of Momentum Equations 346
Conservation of Energy Equation 348
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6-8 Solutions of Convection Equations 
for a Flat Plate 352
The Energy Equation 354
6-9 Nondimensionalized Convection 
Equations and Similarity 356
6-10 Functional Forms of Friction and
Convection Coefficients 357
6-11 Analogies between Momentum
and Heat Transfer 358
Summary 361
References and Suggested Reading 362
Problems 362
C H A P T E R S E V E N
EXTERNAL FORCED CONVECTION 367
7-1 Drag Force and Heat Transfer 
in External Flow 368
Friction and Pressure Drag 368
Heat Transfer 370
7-2 Parallel Flow over Flat Plates 371
Friction Coefficient 372
Heat Transfer Coefficient 373
Flat Plate with Unheated Starting Length 375
Uniform Heat Flux 375
7-3 Flow across Cylinders and Spheres 380
Effect of Surface Roughness 382
Heat Transfer Coefficient 384
7-4 Flow across Tube Banks 389
Pressure Drop 392
Topic of Special Interest:
Reducing Heat Transfer through Surfaces 395
Summary 406
References and Suggested Reading 407
Problems 408
C H A P T E R E I G H T
INTERNAL FORCED CONVECTION 419
8-1 Introduction 420
8-2 Mean Velocity and Mean Temperature 420
Laminar and Turbulent Flow in Tubes 422
8-3 The Entrance Region 423
Entry Lengths 425
8-4 General Thermal Analysis 426
Constant Surface Heat Flux (q·s � constant) 427
Constant Surface Temperature (Ts � constant) 428
8-5 Laminar Flow in Tubes 431
Pressure Drop 433
Temperature Profile and the Nusselt Number 434
Constant Surface Heat Flux 435
Constant Surface Temperature 436
Laminar Flow in Noncircular Tubes 436
Developing Laminar Flow in the Entrance Region 436
8-6 Turbulent Flow in Tubes 441
Rough Surfaces 442
Developing Turbulent Flow in the Entrance Region 443
Turbulent Flow in Noncircular Tubes 443
Flow through Tube Annulus 444
Heat Transfer Enhancement 444
Summary 449
References and Suggested Reading 450
Problems 452
C H A P T E R N I N E
NATURAL CONVECTION 459
9-1 Physical Mechanism of 
Natural Convection 460
9-2 Equation of Motion and 
the Grashof Number 463
The Grashof Number 465
9-3 Natural Convection over Surfaces 466
Vertical Plates (Ts � constant) 467
Vertical Plates (q·s � constant) 467
Vertical Cylinders 467
Inclined Plates 467
Horizontal Plates 469
Horizontal Cylinders and Spheres 469
9-4 Natural Convection from 
Finned Surfaces and PCBs 473
Natural Convection Cooling of Finned Surfaces 
(Ts � constant) 473
Natural Convection Cooling of Vertical PCBs 
(q·s � constant) 474
Mass Flow Rate through the Space between Plates 475
9-5 Natural Convection inside Enclosures 477
Effective Thermal Conductivity 478
Horizontal Rectangular Enclosures 479
Inclined Rectangular Enclosures 479
Vertical Rectangular Enclosures 480
Concentric Cylinders 480
Concentric Spheres 481
Combined Natural Convection and Radiation 481
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CONTENTS
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9-6 Combined Natural and Forced Convection 486
Topic of Special Interest:
Heat Transfer through Windows 489
Summary 499
References and Suggested Reading 500
Problems 501
C H A P T E R T E N
BOILING AND CONDENSATION 515
10-1 Boiling Heat Transfer 516
10-2 Pool Boiling 518
Boiling Regimes and the Boiling Curve 518
Heat Transfer Correlations in Pool Boiling 522
Enhancement of Heat Transfer in Pool Boiling 526
10-3 Flow Boiling 530
10-4 Condensation Heat Transfer 532
10-5 Film Condensation 532
Flow Regimes 534
Heat Transfer Correlations for Film Condensation 535
10-6 Film Condensation Inside 
Horizontal Tubes 545
10-7 Dropwise Condensation 545
Topic of Special Interest:
Heat Pipes 546
Summary 551
References and Suggested Reading 553
Problems 553
C H A P T E R E L E V E N
FUNDAMENTALS OF THERMAL RADIATION 561
11-1 Introduction 562
11-2 Thermal Radiation 563
11-3 Blackbody Radiation 565
11-4 Radiation Intensity 571
Solid Angle 572
Intensity of Emitted Radiation 573
Incident Radiation 574
Radiosity 575
Spectral Quantities 575
11-5 Radiative Properties 577
Emissivity 578
Absorptivity, Reflectivity, and Transmissivity 582
Kirchhoff’s Law 584
The Greenhouse Effect 585
11-6 Atmospheric and Solar Radiation 586
Topic of Special Interest:
Solar Heat Gain through Windows 590
Summary 597
References and Suggested Reading 599
Problems 599
C H A P T E R T W E L V E
RADIATION HEAT TRANSFER 605
12-1 The View Factor 606
12-2 View Factor Relations 609
1 The Reciprocity Relation 610
2 The Summation Rule 613
3 The Superposition Rule 615
4 The Symmetry Rule 616
View Factors between Infinitely Long Surfaces: 
The Crossed-Strings Method 618
12-3 Radiation Heat Transfer: Black Surfaces 620
12-4 Radiation Heat Transfer: 
Diffuse, Gray Surfaces 623
Radiosity 623
Net Radiation Heat Transfer to or from a Surface 623
Net Radiation Heat Transfer between Any 
Two Surfaces 625
Methods of Solving Radiation Problems 626
Radiation Heat Transfer in Two-Surface Enclosures 627
Radiation Heat Transfer in Three-Surface Enclosures 629
12-5 Radiation Shields and the Radiation Effect 635
Radiation Effect on Temperature Measurements 637
12-6 Radiation Exchange with Emitting and
Absorbing Gases 639
Radiation Properties of a Participating Medium 640
Emissivity and Absorptivity of Gases and Gas Mixtures 642
Topic of Special Interest:
Heat Transfer from the Human Body 649
Summary 653
References and Suggested Reading 655
Problems 655
C H A P T E R T H I R T E E N
HEAT EXCHANGERS 667
13-1 Types of Heat Exchangers 668
13-2 The Overall Heat Transfer Coefficient 671
Fouling Factor 674
13-3 Analysis of Heat Exchangers 678
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13-4 The Log Mean Temperature 
Difference Method 680
Counter-Flow Heat Exchangers 682
Multipass and Cross-Flow Heat Exchangers: 
Use of a Correction Factor 683
13-5 The Effectiveness–NTU Method 690
13-6 Selection of Heat Exchangers 700
Heat Transfer Rate 700
Cost 700
Pumping Power 701
Size and Weight 701
Type 701
Materials 701
Other Considerations 702
Summary 703
References and Suggested Reading 704
Problems 705
C H A P T E R F O U R T E E N
MASS TRANSFER 717
14-1 Introduction 718
14-2 Analogy between Heat and Mass Transfer 719
Temperature 720
Conduction 720
Heat Generation 720
Convection 721
14-3 Mass Diffusion 721
1 Mass Basis 722
2 Mole Basis 722
Special Case: Ideal Gas Mixtures 723
Fick’s Law of Diffusion: Stationary Medium Consisting
of Two Species 723
14-4 Boundary Conditions 727
14-5 Steady Mass Diffusion through a Wall 732
14-6 Water Vapor Migration in Buildings 736
14-7 Transient Mass Diffusion 740
14-8 Diffusion in a Moving Medium 743
Special Case: Gas Mixtures at Constant Pressure
and Temperature 747
Diffusion of Vapor through a Stationary Gas: 
Stefan Flow 748
Equimolar Counterdiffusion 750
14-9 Mass Convection 754
Analogy between Friction, Heat Transfer,and Mass
Transfer Coefficients 758
Limitation on the Heat–Mass Convection Analogy 760
Mass Convection Relations 760
14-10 Simultaneous Heat and Mass Transfer 763
Summary 769
References and Suggested Reading 771
Problems 772
C H A P T E R F I F T E E N
COOLING OF ELECTRONIC EQUIPMENT 785
15-1 Introduction and History 786
15-2 Manufacturing of Electronic Equipment 787
The Chip Carrier 787
Printed Circuit Boards 789
The Enclosure 791
15-3 Cooling Load of Electronic Equipment 793
15-4 Thermal Environment 794
15-5 Electronics Cooling in 
Different Applications 795
15-6 Conduction Cooling 797
Conduction in Chip Carriers 798
Conduction in Printed Circuit Boards 803
Heat Frames 805
The Thermal Conduction Module (TCM) 810
15-7 Air Cooling: Natural Convection 
and Radiation 812
15-8 Air Cooling: Forced Convection 820
Fan Selection 823
Cooling Personal Computers 826
15-9 Liquid Cooling 833
15-10 Immersion Cooling 836
Summary 841
References and Suggested Reading 842
Problems 842
A P P E N D I X 1
PROPERTY TABLES AND CHARTS 
(SI UNITS) 855
Table A-1 Molar Mass, Gas Constant, and
Critical-Point Properties 856
Table A-2 Boiling- and Freezing-Point 
Properties 857
Table A-3 Properties of Solid Metals 858
Table A-4 Properties of Solid Nonmetals 861
Table A-5 Properties of Building Materials 862
CONTENTS
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CONTENTS
xii
Table A-6 Properties of Insulating Materials 864
Table A-7 Properties of Common Foods 865
Table A-8 Properties of Miscellaneous 
Materials 867
Table A-9 Properties of Saturated Water 868
Table A-10 Properties of Saturated 
Refrigerant-134a 869
Table A-11 Properties of Saturated Ammonia 870
Table A-12 Properties of Saturated Propane 871
Table A-13 Properties of Liquids 872
Table A-14 Properties of Liquid Metals 873
Table A-15 Properties of Air at 1 atm Pressure 874
Table A-16 Properties of Gases at 1 atm 
Pressure 875
Table A-17 Properties of the Atmosphere at
High Altitude 877
Table A-18 Emissivities of Surfaces 878
Table A-19 Solar Radiative Properties of 
Materials 880
Figure A-20 The Moody Chart for the Friction
Factor for Fully Developed Flow
in Circular Tubes 881
A P P E N D I X 2
PROPERTY TABLES AND CHARTS
(ENGLISH UNITS) 883
Table A-1E Molar Mass, Gas Constant, and
Critical-Point Properties 884
Table A-2E Boiling- and Freezing-Point 
Properties 885
Table A-3E Properties of Solid Metals 886
Table A-4E Properties of Solid Nonmetals 889
Table A-5E Properties of Building Materials 890
Table A-6E Properties of Insulating Materials 892
Table A-7E Properties of Common Foods 893
Table A-8E Properties of Miscellaneous 
Materials 895
Table A-9E Properties of Saturated Water 896
Table A-10E Properties of Saturated 
Refrigerant-134a 897
Table A-11E Properties of Saturated Ammonia 898
Table A-12E Properties of Saturated Propane 899
Table A-13E Properties of Liquids 900
Table A-14E Properties of Liquid Metals 901
Table A-15E Properties of Air at 1 atm Pressure 902
Table A-16E Properties of Gases at 1 atm 
Pressure 903
Table A-17E Properties of the Atmosphere at
High Altitude 905
A P P E N D I X 3
INTRODUCTION TO EES 907
INDEX 921
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C H A P T E R O N E
BASICS OF HEAT TRANSFER 1
Example 1-1 Heating of a Copper Ball 10
Example 1-2 Heating of Water in an 
Electric Teapot 14
Example 1-3 Heat Loss from Heating Ducts 
in a Basement 15
Example 1-4 Electric Heating of a House at
High Elevation 16
Example 1-5 The Cost of Heat Loss through
a Roof 19
Example 1-6 Measuring the Thermal Conductivity
of a Material 23
Example 1-7 Conversion between SI and
English Units 24
Example 1-8 Measuring Convection Heat
Transfer Coefficient 26
Example 1-9 Radiation Effect on 
Thermal Comfort 29
Example 1-10 Heat Loss from a Person 31
Example 1-11 Heat Transfer between
Two Isothermal Plates 32
Example 1-12 Heat Transfer in Conventional
and Microwave Ovens 33
Example 1-13 Heating of a Plate by 
Solar Energy 34
Example 1-14 Solving a System of Equations
with EES 39
C H A P T E R T W O
HEAT CONDUCTION EQUATION 61
Example 2-1 Heat Gain by a Refrigerator 67
Example 2-2 Heat Generation in a 
Hair Dryer 67
Example 2-3 Heat Conduction through the
Bottom of a Pan 72
Example 2-4 Heat Conduction in a
Resistance Heater 72
Example 2-5 Cooling of a Hot Metal Ball 
in Air 73
Example 2-6 Heat Conduction in a 
Short Cylinder 76
Example 2-7 Heat Flux Boundary Condition 80
Example 2-8 Convection and Insulation
Boundary Conditions 82
Example 2-9 Combined Convection and
Radiation Condition 84
Example 2-10 Combined Convection, Radiation,
and Heat Flux 85
Example 2-11 Heat Conduction in a 
Plane Wall 86
Example 2-12 A Wall with Various Sets of
Boundary Conditions 88
Example 2-13 Heat Conduction in the Base Plate
of an Iron 90
Example 2-14 Heat Conduction in a 
Solar Heated Wall 92
Example 2-15 Heat Loss through a 
Steam Pipe 94
Example 2-16 Heat Conduction through a
Spherical Shell 96
Example 2-17 Centerline Temperature of a
Resistance Heater 100
Example 2-18 Variation of Temperature in a
Resistance Heater 100
Example 2-19 Heat Conduction in a Two-Layer
Medium 102
T A B L E O F E X A M P L E S
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CONTENTS
xiv
Example 2-20 Variation of Temperature in a Wall
with k(T) 105
Example 2-21 Heat Conduction through a Wall
with k(T) 106
C H A P T E R T H R E E
STEADY HEAT CONDUCTION 127
Example 3-1 Heat Loss through a Wall 134
Example 3-2 Heat Loss through a 
Single-Pane Window 135
Example 3-3 Heat Loss through 
Double-Pane Windows 136
Example 3-4 Equivalent Thickness for
Contact Resistance 140
Example 3-5 Contact Resistance of 
Transistors 141
Example 3-6 Heat Loss through a 
Composite Wall 144
Example 3-7 Heat Transfer to a
Spherical Container 149
Example 3-8 Heat Loss through an Insulated
Steam Pipe 151
Example 3-9 Heat Loss from an Insulated
Electric Wire 154
Example 3-10 Maximum Power Dissipation of
a Transistor 166
Example 3-11 Selecting a Heat Sink for a 
Transistor 167
Example 3-12 Effect of Fins on Heat Transfer from
Steam Pipes 168
Example 3-13 Heat Loss from Buried 
Steam Pipes 170
Example 3-14 Heat Transfer between Hot and
Cold Water Pipes 173
Example 3-15 Cost of Heat Loss through Walls
in Winter 174
Example 3-16 The R-Value of a Wood 
Frame Wall 179
Example 3-17 The R-Value of a Wall with
Rigid Foam 180
Example 3-18 The R-Value of a Masonry Wall 181
Example 3-19 The R-Value of a Pitched Roof 182
C H A P T E R F O U R
TRANSIENT HEAT CONDUCTION 209
Example 4-1 Temperature Measurement by
Thermocouples 214
Example 4-2 Predicting the Time of Death 215
Example 4-3 Boiling Eggs 224
Example 4-4 Heating of Large Brass Plates 
in an Oven 225
Example 4-5 Cooling of a Long Stainless Steel
Cylindrical Shaft 226
Example 4-6 Minimum Burial Depth of Water
Pipes to Avoid Freezing 230
Example 4-7 Cooling of a Short Brass 
Cylinder 234
Example 4-8 Heat Transfer from a Short 
Cylinder 235
Example 4-9 Cooling of a Long Cylinder 
by Water 236
Example 4-10 Refrigerating Steaks while
Avoiding Frostbite 238
Example 4-11 Chilling of Beef Carcasses in a
Meat Plant 248
C H A P T E R F I V E
NUMERICAL METHODS IN 
HEAT CONDUCTION 265
Example 5-1 Steady Heat Conduction in a Large
Uranium Plate 277
Example 5-2 Heat Transfer from 
Triangular Fins 279
Example 5-3 Steady Two-Dimensional Heat
Conduction in L-Bars 284
Example 5-4 Heat Loss through Chimneys 287
Example 5-5 Transient Heat Conduction in a Large
Uranium Plate 296
Example 5-6 Solar Energy Storage in
Trombe Walls 300
Example 5-7 Transient Two-Dimensional Heat
Conduction in L-Bars 305
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C H A P T E R S I X
FUNDAMENTALS OF CONVECTION 333
Example 6-1 Temperature Rise of Oil in a
Journal Bearing 350
Example 6-2 Finding Convection Coefficient from
Drag Measurement 360
C H A P T E R S E V E N
EXTERNAL FORCED CONVECTION 367
Example 7-1 Flow of Hot Oil over a 
Flat Plate 376
Example 7-2 Cooling of a Hot Block by ForcedAir
at High Elevation 377
Example 7-3 Cooling of Plastic Sheets by
Forced Air 378
Example 7-4 Drag Force Acting on a Pipe 
in a River 383
Example 7-5 Heat Loss from a Steam Pipe 
in Windy Air 386
Example 7-6 Cooling of a Steel Ball by 
Forced Air 387
Example 7-7 Preheating Air by Geothermal Water
in a Tube Bank 393
Example 7-8 Effect of Insulation on
Surface Temperature 402
Example 7-9 Optimum Thickness of 
Insulation 403
C H A P T E R E I G H T
INTERNAL FORCED CONVECTION 419
Example 8-1 Heating of Water in a Tube 
by Steam 430
Example 8-2 Pressure Drop in a Pipe 438
Example 8-3 Flow of Oil in a Pipeline through
a Lake 439
Example 8-4 Pressure Drop in a Water Pipe 445
Example 8-5 Heating of Water by Resistance
Heaters in a Tube 446
Example 8-6 Heat Loss from the Ducts of a
Heating System 448
C H A P T E R N I N E
NATURAL CONVECTION 459
Example 9-1 Heat Loss from Hot 
Water Pipes 470
Example 9-2 Cooling of a Plate in
Different Orientations 471
Example 9-3 Optimum Fin Spacing of a 
Heat Sink 476
Example 9-4 Heat Loss through a Double-Pane
Window 482
Example 9-5 Heat Transfer through a
Spherical Enclosure 483
Example 9-6 Heating Water in a Tube by
Solar Energy 484
Example 9-7 U-Factor for Center-of-Glass Section
of Windows 496
Example 9-8 Heat Loss through Aluminum Framed
Windows 497
Example 9-9 U-Factor of a Double-Door 
Window 498
C H A P T E R T E N
BOILING AND CONDENSATION 515
Example 10-1 Nucleate Boiling Water 
in a Pan 526
Example 10-2 Peak Heat Flux in 
Nucleate Boiling 528
Example 10-3 Film Boiling of Water on a
Heating Element 529
Example 10-4 Condensation of Steam on a
Vertical Plate 541
Example 10-5 Condensation of Steam on a
Tilted Plate 542
Example 10-6 Condensation of Steam on
Horizontal Tubes 543
Example 10-7 Condensation of Steam on
Horizontal Tube Banks 544
CONTENTS
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CONTENTS
xvi
Example 10-8 Replacing a Heat Pipe by a
Copper Rod 550
C H A P T E R E L E V E N
FUNDAMENTALS OF THERMAL RADIATION 561
Example 11-1 Radiation Emission from a 
Black Ball 568
Example 11-2 Emission of Radiation from
a Lightbulb 571
Example 11-3 Radiation Incident on a 
Small Surface 576
Example 11-4 Emissivity of a Surface
and Emissive Power 581
Example 11-5 Selective Absorber and
Reflective Surfaces 589
Example 11-6 Installing Reflective Films
on Windows 596
C H A P T E R T W E L V E
RADIATION HEAT TRANSFER 605
Example 12-1 View Factors Associated with
Two Concentric Spheres 614
Example 12-2 Fraction of Radiation Leaving
through an Opening 615
Example 12-3 View Factors Associated with
a Tetragon 617
Example 12-4 View Factors Associated with a
Triangular Duct 617
Example 12-5 The Crossed-Strings Method for
View Factors 619
Example 12-6 Radiation Heat Transfer in a
Black Furnace 621
Example 12-7 Radiation Heat Transfer between
Parallel Plates 627
Example 12-8 Radiation Heat Transfer in a
Cylindrical Furnace 630
Example 12-9 Radiation Heat Transfer in a
Triangular Furnace 631
Example 12-10 Heat Transfer through a Tubular
Solar Collector 632
Example 12-11 Radiation Shields 638
Example 12-12 Radiation Effect on Temperature
Measurements 639
Example 12-13 Effective Emissivity of
Combustion Gases 646
Example 12-14 Radiation Heat Transfer in a
Cylindrical Furnace 647
Example 12-15 Effect of Clothing on Thermal
Comfort 652
C H A P T E R T H I R T E E N
HEAT EXCHANGERS 667
Example 13-1 Overall Heat Transfer Coefficient of
a Heat Exchanger 675
Example 13-2 Effect of Fouling on the Overall Heat
Transfer Coefficient 677
Example 13-3 The Condensation of Steam in
a Condenser 685
Example 13-4 Heating Water in a Counter-Flow
Heat Exchanger 686
Example 13-5 Heating of Glycerin in a Multipass
Heat Exchanger 687
Example 13-6 Cooling of an 
Automotive Radiator 688
Example 13-7 Upper Limit for Heat Transfer
in a Heat Exchanger 691
Example 13-8 Using the Effectiveness–
NTU Method 697
Example 13-9 Cooling Hot Oil by Water in a
Multipass Heat Exchanger 698
Example 13-10 Installing a Heat Exchanger to Save
Energy and Money 702
C H A P T E R F O U R T E E N
MASS TRANSFER 717
Example 14-1 Determining Mass Fractions from
Mole Fractions 727
Example 14-2 Mole Fraction of Water Vapor at
the Surface of a Lake 728
Example 14-3 Mole Fraction of Dissolved Air
in Water 730
Example 14-4 Diffusion of Hydrogen Gas into
a Nickel Plate 732
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Example 14-5 Diffusion of Hydrogen through a
Spherical Container 735
Example 14-6 Condensation and Freezing of
Moisture in the Walls 738
Example 14-7 Hardening of Steel by the Diffusion
of Carbon 742
Example 14-8 Venting of Helium in the Atmosphere
by Diffusion 751
Example 14-9 Measuring Diffusion Coefficient by
the Stefan Tube 752
Example 14-10 Mass Convection inside a
Circular Pipe 761
Example 14-11 Analogy between Heat and
Mass Transfer 762
Example 14-12 Evaporative Cooling of a
Canned Drink 765
Example 14-13 Heat Loss from Uncovered Hot
Water Baths 766
C H A P T E R F I F T E E N
COOLING OF ELECTRONIC EQUIPMENT 785
Example 15-1 Predicting the Junction Temperature
of a Transistor 788
Example 15-2 Determining the Junction-to-Case
Thermal Resistance 789
Example 15-3 Analysis of Heat Conduction in
a Chip 799
Example 15-4 Predicting the Junction Temperature
of a Device 802
Example 15-5 Heat Conduction along a PCB with
Copper Cladding 804
Example 15-6 Thermal Resistance of an Epoxy
Glass Board 805
Example 15-7 Planting Cylindrical Copper Fillings
in an Epoxy Board 806
Example 15-8 Conduction Cooling of PCBs by a
Heat Frame 807
Example 15-9 Cooling of Chips by the Thermal
Conduction Module 812
Example 15-10 Cooling of a Sealed 
Electronic Box 816
Example 15-11 Cooling of a Component by
Natural Convection 817
Example 15-12 Cooling of a PCB in a Box by
Natural Convection 818
Example 15-13 Forced-Air Cooling of a
Hollow-Core PCB 826
Example 15-14 Forced-Air Cooling of a Transistor
Mounted on a PCB 828
Example 15-15 Choosing a Fan to Cool 
a Computer 830
Example 15-16 Cooling of a Computer 
by a Fan 831
Example 15-17 Cooling of Power Transistors on
a Cold Plate by Water 835
Example 15-18 Immersion Cooling of 
a Logic Chip 840
Example 15-19 Cooling of a Chip by Boiling 840
CONTENTS
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B A S I C S O F H E AT T R A N S F E R
The science of thermodynamics deals with the amount of heat transfer asa system undergoes a process from one equilibrium state to another, andmakes no reference to how long the process will take. But in engineer-
ing, we are often interested in the rate of heat transfer, which is the topic of
the science of heat transfer.
We start this chapter with a review of the fundamental concepts of thermo-
dynamics that form the framework for heat transfer. We first present the
relation of heat to other forms of energy and review the first law of thermo-
dynamics. We then present the three basic mechanisms of heat transfer, which
are conduction, convection, and radiation, and discuss thermal conductivity.
Conduction is the transfer of energy from the more energetic particles of a
substance to the adjacent, less energetic ones as a result of interactions be-
tween the particles. Convection is the mode of heat transfer between a solid
surface and the adjacent liquid or gas that is in motion, and it involves the
combined effects of conduction and fluid motion. Radiation is the energy
emitted by matter in the form of electromagnetic waves (or photons) as a re-
sult of the changes in the electronic configurations of the atoms or molecules.
We close this chapter with a discussion of simultaneous heat transfer.
1
CHAPTER
1
CONTENTS
1–1 Thermodynamics and
Heat Transfer 2
1–2 Engineering Heat Transfer 4
1–3 Heat and Other Forms 
of Energy 6
1–4 The First Law of
Thermodynamics 11
1–5 Heat Transfer 
Mechanisms 17
1–6 Conduction 17
1–7 Convection 25
1–8 Radiation 27
1–9 Simultaneous Heat Transfer
Mechanism 30
1–10 Problem-Solving Technique 35
Topic ofSpecial Interest:
Thermal Comfort 40
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1–1 THERMODYNAMICS AND HEAT TRANSFER
We all know from experience that a cold canned drink left in a room warms up
and a warm canned drink left in a refrigerator cools down. This is accom-
plished by the transfer of energy from the warm medium to the cold one. The
energy transfer is always from the higher temperature medium to the lower
temperature one, and the energy transfer stops when the two mediums reach
the same temperature.
You will recall from thermodynamics that energy exists in various forms. In
this text we are primarily interested in heat, which is the form of energy that
can be transferred from one system to another as a result of temperature dif-
ference. The science that deals with the determination of the rates of such en-
ergy transfers is heat transfer.
You may be wondering why we need to undertake a detailed study on heat
transfer. After all, we can determine the amount of heat transfer for any sys-
tem undergoing any process using a thermodynamic analysis alone. The rea-
son is that thermodynamics is concerned with the amount of heat transfer as a
system undergoes a process from one equilibrium state to another, and it gives
no indication about how long the process will take. A thermodynamic analysis
simply tells us how much heat must be transferred to realize a specified
change of state to satisfy the conservation of energy principle.
In practice we are more concerned about the rate of heat transfer (heat trans-
fer per unit time) than we are with the amount of it. For example, we can de-
termine the amount of heat transferred from a thermos bottle as the hot coffee
inside cools from 90°C to 80°C by a thermodynamic analysis alone. But a typ-
ical user or designer of a thermos is primarily interested in how long it will be
before the hot coffee inside cools to 80°C, and a thermodynamic analysis can-
not answer this question. Determining the rates of heat transfer to or from a
system and thus the times of cooling or heating, as well as the variation of the
temperature, is the subject of heat transfer (Fig. 1–1).
Thermodynamics deals with equilibrium states and changes from one equi-
librium state to another. Heat transfer, on the other hand, deals with systems
that lack thermal equilibrium, and thus it is a nonequilibrium phenomenon.
Therefore, the study of heat transfer cannot be based on the principles of
thermodynamics alone. However, the laws of thermodynamics lay the frame-
work for the science of heat transfer. The first law requires that the rate of
energy transfer into a system be equal to the rate of increase of the energy of
that system. The second law requires that heat be transferred in the direction
of decreasing temperature (Fig. 1–2). This is like a car parked on an inclined
road that must go downhill in the direction of decreasing elevation when its
brakes are released. It is also analogous to the electric current flowing in the
direction of decreasing voltage or the fluid flowing in the direction of de-
creasing total pressure.
The basic requirement for heat transfer is the presence of a temperature dif-
ference. There can be no net heat transfer between two mediums that are at the
same temperature. The temperature difference is the driving force for heat
transfer, just as the voltage difference is the driving force for electric current
flow and pressure difference is the driving force for fluid flow. The rate of heat
transfer in a certain direction depends on the magnitude of the temperature
gradient (the temperature difference per unit length or the rate of change of
�
2
HEAT TRANSFER
Hot
coffee
Thermos
bottle
Insulation
FIGURE 1–1
We are normally interested in how long
it takes for the hot coffee in a thermos to
cool to a certain temperature, which
cannot be determined from a
thermodynamic analysis alone.
Heat
Cool
environment
20°CHot
coffee
70°C
FIGURE 1–2
Heat flows in the direction of
decreasing temperature.
cen58933_ch01.qxd 9/10/2002 8:29 AM Page 2
temperature) in that direction. The larger the temperature gradient, the higher
the rate of heat transfer.
Application Areas of Heat Transfer
Heat transfer is commonly encountered in engineering systems and other as-
pects of life, and one does not need to go very far to see some application ar-
eas of heat transfer. In fact, one does not need to go anywhere. The human
body is constantly rejecting heat to its surroundings, and human comfort is
closely tied to the rate of this heat rejection. We try to control this heat trans-
fer rate by adjusting our clothing to the environmental conditions.
Many ordinary household appliances are designed, in whole or in part, by
using the principles of heat transfer. Some examples include the electric or gas
range, the heating and air-conditioning system, the refrigerator and freezer, the
water heater, the iron, and even the computer, the TV, and the VCR. Of course,
energy-efficient homes are designed on the basis of minimizing heat loss in
winter and heat gain in summer. Heat transfer plays a major role in the design
of many other devices, such as car radiators, solar collectors, various compo-
nents of power plants, and even spacecraft. The optimal insulation thickness
in the walls and roofs of the houses, on hot water or steam pipes, or on water
heaters is again determined on the basis of a heat transfer analysis with eco-
nomic consideration (Fig. 1–3).
Historical Background
Heat has always been perceived to be something that produces in us a sensa-
tion of warmth, and one would think that the nature of heat is one of the first
things understood by mankind. But it was only in the middle of the nineteenth
CHAPTER 1
3
FIGURE 1–3
Some application areas of heat transfer.
Refrigeration systemsPower plantsCar radiators
Water out
Water in
Circuit boardsAir-conditioning
systems
The human body
cen58933_ch01.qxd 9/10/2002 8:29 AM Page 3
century that we had a true physical understanding of the nature of heat, thanks
to the development at that time of the kinetic theory, which treats molecules
as tiny balls that are in motion and thus possess kinetic energy. Heat is then
defined as the energy associated with the random motion of atoms and mole-
cules. Although it was suggested in the eighteenth and early nineteenth cen-
turies that heat is the manifestation of motion at the molecular level (called the
live force), the prevailing view of heat until the middle of the nineteenth cen-
tury was based on the caloric theory proposed by the French chemist Antoine
Lavoisier (1743–1794) in 1789. The caloric theory asserts that heat is a fluid-
like substance called the caloric that is a massless, colorless, odorless, and
tasteless substance that can be poured from one body into another (Fig. 1–4).
When caloric was added to a body, its temperature increased; and when
caloric was removed from a body, its temperature decreased. When a body
could not contain any more caloric, much the same way as when a glass of
water could not dissolve any more salt or sugar, the body was said to be satu-
rated with caloric. This interpretation gave rise to the terms saturated liquid
and saturated vapor that are still in use today.
The caloric theory came under attack soon after its introduction. It main-
tained that heat is a substance that could not be created or destroyed. Yet it
was known that heat can be generated indefinitely by rubbing one’s hands to-
gether or rubbing two pieces of wood together. In 1798, the American Ben-
jamin Thompson (Count Rumford) (1753–1814) showed in his papers that
heat can be generated continuously through friction. The validity of the caloric
theory was also challenged by several others. But it was the careful experi-
ments of the Englishman James P. Joule (1818–1889) published in 1843 that
finally convinced the skeptics that heat was not a substance after all, and thus
put the caloric theory to rest. Although the caloric theory was totally aban-
donedin the middle of the nineteenth century, it contributed greatly to the de-
velopment of thermodynamics and heat transfer.
1–2 ENGINEERING HEAT TRANSFER
Heat transfer equipment such as heat exchangers, boilers, condensers, radia-
tors, heaters, furnaces, refrigerators, and solar collectors are designed pri-
marily on the basis of heat transfer analysis. The heat transfer problems
encountered in practice can be considered in two groups: (1) rating and
(2) sizing problems. The rating problems deal with the determination of the
heat transfer rate for an existing system at a specified temperature difference.
The sizing problems deal with the determination of the size of a system in
order to transfer heat at a specified rate for a specified temperature difference.
A heat transfer process or equipment can be studied either experimentally
(testing and taking measurements) or analytically (by analysis or calcula-
tions). The experimental approach has the advantage that we deal with the
actual physical system, and the desired quantity is determined by measure-
ment, within the limits of experimental error. However, this approach is ex-
pensive, time-consuming, and often impractical. Besides, the system we are
analyzing may not even exist. For example, the size of a heating system of
a building must usually be determined before the building is actually built
on the basis of the dimensions and specifications given. The analytical ap-
proach (including numerical approach) has the advantage that it is fast and
�
4
HEAT TRANSFER
Hot
body
Cold
body
Contact
surface
Caloric
FIGURE 1–4
In the early nineteenth century, heat was
thought to be an invisible fluid called the
caloric that flowed from warmer bodies
to the cooler ones.
cen58933_ch01.qxd 9/10/2002 8:29 AM Page 4
inexpensive, but the results obtained are subject to the accuracy of the
assumptions and idealizations made in the analysis. In heat transfer studies,
often a good compromise is reached by reducing the choices to just a few by
analysis, and then verifying the findings experimentally.
Modeling in Heat Transfer
The descriptions of most scientific problems involve expressions that relate
the changes in some key variables to each other. Usually the smaller the
increment chosen in the changing variables, the more general and accurate
the description. In the limiting case of infinitesimal or differential changes in
variables, we obtain differential equations that provide precise mathematical
formulations for the physical principles and laws by representing the rates of
changes as derivatives. Therefore, differential equations are used to investi-
gate a wide variety of problems in sciences and engineering, including heat
transfer. However, most heat transfer problems encountered in practice can be
solved without resorting to differential equations and the complications asso-
ciated with them.
The study of physical phenomena involves two important steps. In the first
step, all the variables that affect the phenomena are identified, reasonable as-
sumptions and approximations are made, and the interdependence of these
variables is studied. The relevant physical laws and principles are invoked,
and the problem is formulated mathematically. The equation itself is very in-
structive as it shows the degree of dependence of some variables on others,
and the relative importance of various terms. In the second step, the problem
is solved using an appropriate approach, and the results are interpreted.
Many processes that seem to occur in nature randomly and without any or-
der are, in fact, being governed by some visible or not-so-visible physical
laws. Whether we notice them or not, these laws are there, governing consis-
tently and predictably what seem to be ordinary events. Most of these laws are
well defined and well understood by scientists. This makes it possible to pre-
dict the course of an event before it actually occurs, or to study various aspects
of an event mathematically without actually running expensive and time-
consuming experiments. This is where the power of analysis lies. Very accu-
rate results to meaningful practical problems can be obtained with relatively
little effort by using a suitable and realistic mathematical model. The prepara-
tion of such models requires an adequate knowledge of the natural phenomena
involved and the relevant laws, as well as a sound judgment. An unrealistic
model will obviously give inaccurate and thus unacceptable results.
An analyst working on an engineering problem often finds himself or her-
self in a position to make a choice between a very accurate but complex
model, and a simple but not-so-accurate model. The right choice depends on
the situation at hand. The right choice is usually the simplest model that yields
adequate results. For example, the process of baking potatoes or roasting a
round chunk of beef in an oven can be studied analytically in a simple way by
modeling the potato or the roast as a spherical solid ball that has the properties
of water (Fig. 1–5). The model is quite simple, but the results obtained are suf-
ficiently accurate for most practical purposes. As another example, when we
analyze the heat losses from a building in order to select the right size for a
heater, we determine the heat losses under anticipated worst conditions and
select a furnace that will provide sufficient heat to make up for those losses.
CHAPTER 1
5
Oven
Ideal
175°C
Water
Potato Actual
FIGURE 1–5
Modeling is a powerful engineering
tool that provides great insight and
simplicity at the expense of
some accuracy.
cen58933_ch01.qxd 9/10/2002 8:29 AM Page 5
Often we tend to choose a larger furnace in anticipation of some future ex-
pansion, or just to provide a factor of safety. A very simple analysis will be ad-
equate in this case.
When selecting heat transfer equipment, it is important to consider the ac-
tual operating conditions. For example, when purchasing a heat exchanger
that will handle hard water, we must consider that some calcium deposits will
form on the heat transfer surfaces over time, causing fouling and thus a grad-
ual decline in performance. The heat exchanger must be selected on the basis
of operation under these adverse conditions instead of under new conditions.
Preparing very accurate but complex models is usually not so difficult. But
such models are not much use to an analyst if they are very difficult and time-
consuming to solve. At the minimum, the model should reflect the essential
features of the physical problem it represents. There are many significant real-
world problems that can be analyzed with a simple model. But it should al-
ways be kept in mind that the results obtained from an analysis are as accurate
as the assumptions made in simplifying the problem. Therefore, the solution
obtained should not be applied to situations for which the original assump-
tions do not hold.
A solution that is not quite consistent with the observed nature of the prob-
lem indicates that the mathematical model used is too crude. In that case, a
more realistic model should be prepared by eliminating one or more of the
questionable assumptions. This will result in a more complex problem that, of
course, is more difficult to solve. Thus any solution to a problem should be in-
terpreted within the context of its formulation.
1–3 HEAT AND OTHER FORMS OF ENERGY
Energy can exist in numerous forms such as thermal, mechanical, kinetic, po-
tential, electrical, magnetic, chemical, and nuclear, and their sum constitutes
the total energy E (or e on a unit mass basis) of a system. The forms of energy
related to the molecular structure of a system and the degree of the molecular
activity are referred to as the microscopic energy. The sum of all microscopic
forms of energy is called the internal energy of a system, and is denoted by
U (or u on a unit mass basis).
The international unit of energy is joule (J) or kilojoule (1 kJ � 1000 J).
In the English system, the unit ofenergy is the British thermal unit (Btu),
which is defined as the energy needed to raise the temperature of 1 lbm of
water at 60°F by 1°F. The magnitudes of kJ and Btu are almost identical
(1 Btu � 1.055056 kJ). Another well-known unit of energy is the calorie
(1 cal � 4.1868 J), which is defined as the energy needed to raise the temper-
ature of 1 gram of water at 14.5°C by 1°C.
Internal energy may be viewed as the sum of the kinetic and potential ener-
gies of the molecules. The portion of the internal energy of a system asso-
ciated with the kinetic energy of the molecules is called sensible energy or
sensible heat. The average velocity and the degree of activity of the mole-
cules are proportional to the temperature. Thus, at higher temperatures the
molecules will possess higher kinetic energy, and as a result, the system will
have a higher internal energy.
The internal energy is also associated with the intermolecular forces be-
tween the molecules of a system. These are the forces that bind the molecules
�
6
HEAT TRANSFER
cen58933_ch01.qxd 9/10/2002 8:29 AM Page 6
to each other, and, as one would expect, they are strongest in solids and weak-
est in gases. If sufficient energy is added to the molecules of a solid or liquid,
they will overcome these molecular forces and simply break away, turning the
system to a gas. This is a phase change process and because of this added en-
ergy, a system in the gas phase is at a higher internal energy level than it is in
the solid or the liquid phase. The internal energy associated with the phase of
a system is called latent energy or latent heat.
The changes mentioned above can occur without a change in the chemical
composition of a system. Most heat transfer problems fall into this category,
and one does not need to pay any attention to the forces binding the atoms in
a molecule together. The internal energy associated with the atomic bonds in
a molecule is called chemical (or bond) energy, whereas the internal energy
associated with the bonds within the nucleus of the atom itself is called nu-
clear energy. The chemical and nuclear energies are absorbed or released dur-
ing chemical or nuclear reactions, respectively.
In the analysis of systems that involve fluid flow, we frequently encounter
the combination of properties u and Pv. For the sake of simplicity and conve-
nience, this combination is defined as enthalpy h. That is, h � u � Pv where
the term Pv represents the flow energy of the fluid (also called the flow work),
which is the energy needed to push a fluid and to maintain flow. In the energy
analysis of flowing fluids, it is convenient to treat the flow energy as part of
the energy of the fluid and to represent the microscopic energy of a fluid
stream by enthalpy h (Fig. 1–6).
Specific Heats of Gases, Liquids, and Solids
You may recall that an ideal gas is defined as a gas that obeys the relation
Pv � RT or P � �RT (1-1)
where P is the absolute pressure, v is the specific volume, T is the absolute
temperature, � is the density, and R is the gas constant. It has been experi-
mentally observed that the ideal gas relation given above closely approxi-
mates the P-v-T behavior of real gases at low densities. At low pressures and
high temperatures, the density of a gas decreases and the gas behaves like an
ideal gas. In the range of practical interest, many familiar gases such as air,
nitrogen, oxygen, hydrogen, helium, argon, neon, and krypton and even heav-
ier gases such as carbon dioxide can be treated as ideal gases with negligible
error (often less than one percent). Dense gases such as water vapor in
steam power plants and refrigerant vapor in refrigerators, however, should not
always be treated as ideal gases since they usually exist at a state near
saturation.
You may also recall that specific heat is defined as the energy required to
raise the temperature of a unit mass of a substance by one degree (Fig. 1–7).
In general, this energy depends on how the process is executed. In thermo-
dynamics, we are interested in two kinds of specific heats: specific heat at
constant volume Cv and specific heat at constant pressure Cp. The specific
heat at constant volume Cv can be viewed as the energy required to raise the
temperature of a unit mass of a substance by one degree as the volume is held
constant. The energy required to do the same as the pressure is held constant
is the specific heat at constant pressure Cp. The specific heat at constant
CHAPTER 1
7
Stationary
fluid
Energy = h
Energy = u
Flowing
fluid
FIGURE 1–6
The internal energy u represents the mi-
croscopic energy of a nonflowing fluid,
whereas enthalpy h represents the micro-
scopic energy of a flowing fluid.
5 kJ
m = 1 kg
∆T = 1°C
Specific heat = 5 kJ/kg·°C
FIGURE 1–7
Specific heat is the energy required to
raise the temperature of a unit mass
of a substance by one degree in a
specified way.
cen58933_ch01.qxd 9/10/2002 8:29 AM Page 7
pressure Cp is greater than Cv because at constant pressure the system is al-
lowed to expand and the energy for this expansion work must also be supplied
to the system. For ideal gases, these two specific heats are related to each
other by Cp � Cv � R.
A common unit for specific heats is kJ/kg · °C or kJ/kg · K. Notice that these
two units are identical since ∆T(°C) � ∆T(K), and 1°C change in temperature
is equivalent to a change of 1 K. Also, 
1 kJ/kg · °C � 1 J/g · °C � 1 kJ/kg · K � 1 J/g · K
The specific heats of a substance, in general, depend on two independent
properties such as temperature and pressure. For an ideal gas, however, they
depend on temperature only (Fig. 1–8). At low pressures all real gases ap-
proach ideal gas behavior, and therefore their specific heats depend on tem-
perature only.
The differential changes in the internal energy u and enthalpy h of an ideal
gas can be expressed in terms of the specific heats as
du � Cv dT and dh � Cp dT (1-2)
The finite changes in the internal energy and enthalpy of an ideal gas during a
process can be expressed approximately by using specific heat values at the
average temperature as
�u � Cv, ave�T and �h � Cp, ave�T (J/g) (1-3)
or
�U � mCv, ave�T and �H � mCp, ave�T (J) (1-4)
where m is the mass of the system.
A substance whose specific volume (or density) does not change with tem-
perature or pressure is called an incompressible substance. The specific vol-
umes of solids and liquids essentially remain constant during a process, and
thus they can be approximated as incompressible substances without sacrific-
ing much in accuracy.
The constant-volume and constant-pressure specific heats are identical for
incompressible substances (Fig. 1–9). Therefore, for solids and liquids the
subscripts on Cv and Cp can be dropped and both specific heats can be rep-
resented by a single symbol, C. That is, Cp � Cv � C. This result could also
be deduced from the physical definitions of constant-volume and constant-
pressure specific heats. Specific heats of several common gases, liquids, and
solids are given in the Appendix.
The specific heats of incompressible substances depend on temperature
only. Therefore, the change in the internal energy of solids and liquids can be
expressed as
�U � mCave�T (J) (1-5)
8
THERMODYNAMICS
0.718 kJ 0.855 kJ
Air
m = 1 kg
300 → 301 K
Air
m = 1 kg
1000 → 1001 K
FIGURE 1–8
The specific heat of a substance changes
with temperature.
IRON
25°C
= Cv = Cp
= 0.45 kJ/kg·°C
C 
FIGURE 1–9
The Cv and Cp values of incompressible
substances are identical and are
denoted by C.
cen58933_ch01.qxd 9/10/2002 8:29 AM Page 8
where Cave is the average specific heat evaluated at the average temperature.
Note that the internal energy change of the systems that remain in a single
phase (liquid, solid, or gas) during the process can be determined very easily
using average specific heats.
Energy Transfer
Energy can be transferred to or from a given mass by two mechanisms: heat
Q and work W. An energy interaction is heat transferif its driving force is a
temperature difference. Otherwise, it is work. A rising piston, a rotating shaft,
and an electrical wire crossing the system boundaries are all associated with
work interactions. Work done per unit time is called power, and is denoted
by W
·
. The unit of power is W or hp (1 hp � 746 W). Car engines and hy-
draulic, steam, and gas turbines produce work; compressors, pumps, and
mixers consume work. Notice that the energy of a system decreases as it does
work, and increases as work is done on it.
In daily life, we frequently refer to the sensible and latent forms of internal
energy as heat, and we talk about the heat content of bodies (Fig. 1–10). In
thermodynamics, however, those forms of energy are usually referred to as
thermal energy to prevent any confusion with heat transfer.
The term heat and the associated phrases such as heat flow, heat addition,
heat rejection, heat absorption, heat gain, heat loss, heat storage, heat gener-
ation, electrical heating, latent heat, body heat, and heat source are in com-
mon use today, and the attempt to replace heat in these phrases by thermal
energy had only limited success. These phrases are deeply rooted in our vo-
cabulary and they are used by both the ordinary people and scientists without
causing any misunderstanding. For example, the phrase body heat is under-
stood to mean the thermal energy content of a body. Likewise, heat flow is
understood to mean the transfer of thermal energy, not the flow of a fluid-like
substance called heat, although the latter incorrect interpretation, based on the
caloric theory, is the origin of this phrase. Also, the transfer of heat into a sys-
tem is frequently referred to as heat addition and the transfer of heat out of a
system as heat rejection.
Keeping in line with current practice, we will refer to the thermal energy as
heat and the transfer of thermal energy as heat transfer. The amount of heat
transferred during the process is denoted by Q. The amount of heat transferred
per unit time is called heat transfer rate, and is denoted by Q· . The overdot
stands for the time derivative, or “per unit time.” The heat transfer rate Q
·
has
the unit J/s, which is equivalent to W.
When the rate of heat transfer Q
·
is available, then the total amount of heat
transfer Q during a time interval �t can be determined from
Q � Q
·
dt (J) (1-6)
provided that the variation of Q
·
with time is known. For the special case of
Q
·
� constant, the equation above reduces to
Q � Q
·
�t (J) (1-7)
��t
0
CHAPTER 1
9
Vapor
80°C
Liquid
80°C
25°C
Heat
transfer
FIGURE 1–10
The sensible and latent forms of internal
energy can be transferred as a result of
a temperature difference, and they are
referred to as heat or thermal energy.
cen58933_ch01.qxd 9/10/2002 8:29 AM Page 9
The rate of heat transfer per unit area normal to the direction of heat transfer
is called heat flux, and the average heat flux is expressed as (Fig. 1–11)
q· � (W/m2) (1-8)
where A is the heat transfer area. The unit of heat flux in English units is
Btu/h · ft2. Note that heat flux may vary with time as well as position on a
surface.
Q·
A
10
HEAT TRANSFER
3 m
2 m
A = 6 m2
Q = 24 W
 = const.
.
.
.
q = = = 4 W/m2 
Q
—
A
24 W–——
6 m2
FIGURE 1–11
Heat flux is heat transfer per unit
time and per unit area, and is equal
to q· � Q
·
/A when Q
·
is uniform over
the area A.
T2 = 150°C
A = D2π
T1 = 100°C
Q
FIGURE 1–12
Schematic for Example 1–1.
EXAMPLE 1–1 Heating of a Copper Ball
A 10-cm diameter copper ball is to be heated from 100°C to an average tem-
perature of 150°C in 30 minutes (Fig. 1–12). Taking the average density and
specific heat of copper in this temperature range to be � � 8950 kg/m3 and
Cp � 0.395 kJ/kg · °C, respectively, determine (a) the total amount of heat
transfer to the copper ball, (b) the average rate of heat transfer to the ball, and
(c) the average heat flux.
SOLUTION The copper ball is to be heated from 100°C to 150°C. The total
heat transfer, the average rate of heat transfer, and the average heat flux are to
be determined.
Assumptions Constant properties can be used for copper at the average
temperature.
Properties The average density and specific heat of copper are given to be
� � 8950 kg/m3 and Cp � 0.395 kJ/kg · °C.
Analysis (a) The amount of heat transferred to the copper ball is simply the
change in its internal energy, and is determined from
Energy transfer to the system � Energy increase of the system
Q � �U � mCave (T2 � T1)
where
m � �V � �D3 � (8950 kg/m3)(0.1 m)3 � 4.69 kg
Substituting, 
Q � (4.69 kg)(0.395 kJ/kg · °C)(150 � 100)°C � 92.6 kJ
Therefore, 92.6 kJ of heat needs to be transferred to the copper ball to heat it
from 100°C to 150°C.
(b) The rate of heat transfer normally changes during a process with time. How-
ever, we can determine the average rate of heat transfer by dividing the total
amount of heat transfer by the time interval. Therefore, 
Q
·
ave � � � 0.0514 kJ/s � 51.4 W
92.6 kJ
1800 s
Q
�t
�
6
�
6
cen58933_ch01.qxd 9/10/2002 8:29 AM Page 10
1–4 THE FIRST LAW OF THERMODYNAMICS
The first law of thermodynamics, also known as the conservation of energy
principle, states that energy can neither be created nor destroyed; it can only
change forms. Therefore, every bit of energy must be accounted for during a
process. The conservation of energy principle (or the energy balance) for any
system undergoing any process may be expressed as follows: The net change
(increase or decrease) in the total energy of the system during a process is
equal to the difference between the total energy entering and the total energy
leaving the system during that process. That is, 
(1-9)
Noting that energy can be transferred to or from a system by heat, work, and
mass flow, and that the total energy of a simple compressible system consists
of internal, kinetic, and potential energies, the energy balance for any system
undergoing any process can be expressed as
Ein � Eout � �Esystem (J) (1-10)14243 123
Net energy transfer Change in internal, kinetic,
by heat, work, and mass potential, etc., energies
or, in the rate form, as
E
·
in � E
·
out � dEsystem/dt (W) (1-11)14243 14243
Rate of net energy transfer Rate of change in internal
by heat, work, and mass kinetic, potential, etc., energies
Energy is a property, and the value of a property does not change unless the
state of the system changes. Therefore, the energy change of a system is zero
(�Esystem � 0) if the state of the system does not change during the process,
that is, the process is steady. The energy balance in this case reduces to
(Fig. 1–13)
Steady, rate form: E
·
in � E
·
out (1-12)123 123
Rate of net energy transfer in Rate of net energy transfer out
by heat, work, and mass by heat, work, and mass
In the absence of significant electric, magnetic, motion, gravity, and surface
tension effects (i.e., for stationary simple compressible systems), the change
�Total energyentering thesystem � � �
Total energy
leaving the
system � � �
Change in the
total energy of
the system �
�
CHAPTER 1
11
Heat
Work
Mass
Steady
system
Ein = Eout
Heat
Work
Mass
· ·
Ein
·
Eout
·
FIGURE 1–13
In steady operation, the rate of energy
transfer to a system is equal to the rate
of energy transfer from the system.
(c) Heat flux is defined as the heat transfer per unit time per unit area, or the
rate of heat transfer per unit area. Therefore, the average heat flux in this
case is
q·ave � � � � 1636 W/m2
Discussion Note that heat flux may vary with location on a surface. The value
calculated above is the average heat flux over the entire surface of the ball.
51.4 W
�(0.1 m)2
Q· ave
�D2
Q· ave
A
cen58933_ch01.qxd 9/10/2002 8:29 AM Page 11
in the total energy of a system during a process is simply the change in its in-
ternal energy. That is, �Esystem � �Usystem.
In heat transfer analysis, we are usually interested only in the forms of en-
ergy that can be transferred